Problem: Solve for $x$ : $2\sqrt{x} + 3 = 9\sqrt{x} + 4$
Solution: Subtract $2\sqrt{x}$ from both sides: $(2\sqrt{x} + 3) - 2\sqrt{x} = (9\sqrt{x} + 4) - 2\sqrt{x}$ $3 = 7\sqrt{x} + 4$ Subtract $4$ from both sides: $3 - 4 = (7\sqrt{x} + 4) - 4$ $-1 = 7\sqrt{x}$ Divide both sides by $7$ $\frac{-1}{7} = \frac{7\sqrt{x}}{7}$ Simplify. $-\dfrac{1}{7} = \sqrt{x}$ The principal root of a number cannot be negative. So, there is no solution.